What do noble Romans, such as Cassius and Flavius, fear or resent about Caesar's successes in Shakespeare's Julius Caesar?

Early in act 1, scene 2, of Shakespeare's Julius Caesar,Cassius and Brutus express fear that Caesar will be made king, leading to the fall of the Roman Republic. They express their fear when, at the games, they hear the crowd calling for Caesar to be made king and soon learn thereafter that Antony had offered him a crown three times. Though Caesar rejected the crown all three times, the Conspirators feel that he...

Early in act 1, scene 2, of Shakespeare's Julius Caesar, Cassius and Brutus express fear that Caesar will be made king, leading to the fall of the Roman Republic. They express their fear when, at the games, they hear the crowd calling for Caesar to be made king and soon learn thereafter that Antony had offered him a crown three times. Though Caesar rejected the crown all three times, the Conspirators feel that he was loath to reject it as a result of his rising arrogance and soon may not reject it.

Cassius takes his fear one step further when he recounts a story in which, while crossing the stormy Tiber together, Caesar nearly gave up in exhaustion and called out to Cassius, "Help me, Cassius, or I sink!" (1.2.111). In Cassius's view, the people of Rome now think of the weak and frail man Caesar as a god. Cassius revolts at Caesar's arrogance and is jealous at the thought of having to bow before Caesar, jealous of Caesar's power. We particularly see Cassius express jealousy over Caesar's power when he asks Brutus the following, upon hearing the people shout in exultation as more honors were bestowed on Caesar:

Brutus and Caesar: what should be in that "Caesar"?
Why should that name be sounded more than yours? (1.2.142-43)

The conspirators are jealous of Caesar's power because they know that if he is made king, their roles as senators in the Senate will be rendered powerless.

Similarly, like all the conspirators, Flavius is jealous of Caesar's power and wants to protect the Senate from Caesar's dictatorship. While Flavius is not in the play much, in act 1, scene 1, we see him and Marullus chastise commoners for wanting to pay honors to Caesar on Caesar's holiday. They chastise them by calling them hypocrites through pointing out that they paid the exact same honors to Pompey who has now been slain by Caesar. Their point is to assert that if they honored Pompey, then surely they can't legitimately honor Caesar who has killed Pompey. Flavius then commands the commoners to gather themselves together by the banks of the Tiber to weep for the fall of Pompey. We can deduce based on this that Flavius was a strong supporter of Pompey as a protector of the Republic and now fears that Caesar will destroy the Republic.